A Variable Density Topology Optimization Method For Continuum Structure With Smooth Boundary And Its Application In Bridge Selection

With the rapid development of computer technology,the research of structural topology optimization should be applied to become one of the most valuable topics in the field of structural optimization,and also become one of the most challenging research directions in the field of structural design.The main idea of structural topology optimization is to distribute finite materials to the design domain reasonably through cyclic calculation,so as to achieve the optimal performance of the structure.At first,structural optimization is only limited to mechanical structure design.After years of development,structural optimization has now expanded to physics,fluid,dynamics,aerospace and heat conduction and other disciplines.With the increasing frequency of steel structure in the building,civil engineering will usher in a new era of topology optimization.However,at present,there are still many problems in topology optimization,such as optimization efficiency,gray-scale unit,zigzag boundary and so on.Therefore,the main work of this paper is to use a density evolution topology optimization method of continuum structure with smooth boundary to solve some key problems in structure design.Firstly,in the second chapter,a variable density topology optimization method for irregular continuum structures with smooth boundaries is proposed.On the one hand,the main feature of this method is to delete the element with density of 0 in the optimization process,which can significantly improve the calculation efficiency of optimization.On the other hand,after the finite element model of optimization results is obtained,the element density is further transformed into node density,and the level set of node density is used to display the optimization result.The optimized result has smooth boundary and can be directly saved as the 3D model of STL,which can be further produced by 3D printing.In addition,if the boundary needs to be further smoothed,the optimized finite element model can be subdivided,and then the refined node density level set is used to display,so the boundary of the optimized model will be smoother.Secondly,the topology optimization of irregular continuum structures under nonstationary random excitation is studied in the third chapter.Based on the idea of time domain explicit method,the explicit expressions of structural dynamic response and its variance under random excitation are derived by combining mode acceleration method and Newmark-β method.The explicit expression of the sensitivity of the maximum displacement variance to the design variables is obtained by using the time domain explicit adjoint method.Then,the initial structure finite element model is established by ANSYS software,and then the optimization model is established with the maximum degree of freedom of the structure and the minimum variance of the displacement.Combined with the improved variable density method,the optimization problem is solved.The feasibility and correctness of the optimization method are proved by an example.Finally,based on the actual structural engineering,the fourth chapter analyzes the concept of the main structure of the arch bridge.By changing the constraint conditions of the structure,the improved variable density method is used to optimize the topology of the main structure of the arch bridge.After static analysis and static plus dynamic analysis,the optimal structure is found and the conceptual design of the arch bridge is preliminarily completed It provides a reference for the actual engineering design and selection.